Test-suite minimization is one key technique for optimizing the software testing process. Due to the need to balance multiple factors, multi-criteria test-suite minimization (MCTSM) becomes a popular research topic in the recent decade. The MCTSM problem is typically modeled as integer linear programming (ILP) problem and solved with weighted-sum single objective approach. However, there is no existing approach that can generate sound (i.e., being Pareto-optimal) and complete (i.e., covering the entire Pareto front) Pareto-optimal solution set, to the knowledge of the authors. In this work, we first prove that the ILP formulation can accurately model the MCTSM problem and then propose the multi-objective integer programming (MOIP) approaches to solve it. We apply our MOIP approaches on three specific MCTSM problems and compare the results with those of the cutting-edge methods, namely, NonlinearFormulation_LinearSolver (NF_LS) and two Multi-Objective Evolutionary Algorithms (MOEAs). The results show that our MOIP approaches can always find sound and complete solutions on five subject programs, using similar or significantly less time than NF_LS and two MOEAs do. The current experimental results are quite promising, and our approaches have the potential to be applied for other similar search-based software engineering problems.

中文翻译：

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求解多准则测试套件最小化问题的多目标整数规划方法

测试套件最小化是优化软件测试过程的一项关键技术。由于需要平衡多种因素，多标准测试套件最小化（MCTSM）成为近十年来的热门研究课题。MCTSM 问题通常建模为整数线性规划 (ILP) 问题，并使用加权和单目标方法求解。然而，据作者所知，没有现有的方法可以产生声音（即帕累托最优）和完整（即覆盖整个帕累托前沿）帕累托最优解集。在这项工作中，我们首先证明 ILP 公式可以准确地模拟 MCTSM 问题，然后提出多目标整数规划 (MOIP) 方法来解决它。NonlinearFormulation_LinearSolver(NF_LS) 和两个多目标进化算法 (MOEA)。结果表明，与 NF_LS 和两个 MOEA 相比，我们的 MOIP 方法始终可以在五个主题程序上找到合理且完整的解决方案，使用相似或明显更少的时间。目前的实验结果很有希望，我们的方法有可能应用于其他类似的基于搜索的软件工程问题。